I use a cheap car wash soap to try and wash off the major stuff first.
Then I take apart the bike, piece by piece. I really know no other way.

I clean and lube each part that came off, replacing the consumables as needed.

The frame is an issue by itself, and can best be dealt with by having no attachments, as an entity of its own.

Once that is done, reassemble with clean components.

My choice of cleaning supplies is Purple Stuff, WD40, Bleche-White, a toothbrush or three, some 0000 steel wool, and Dawn dishwashing liquid. I use shop rags, q-tips, and towels. I also use solvent to wash some parts (mainly cassettes and freewheels).

I stole a ShamWow from drrobwave, and that's fairly handy, but it kind of creeps me out because it's clingy.

For frames, I like Sharpie paint pens (med and fine point), Testor's enamel, hobby clearcoat, and various fingernail polishes mixed to color.

I also have rubbing compound and paste wax.

Not many things substitute for elbow grease and attention to detail. That requires Yeungling.

Thank you for allowing me to mix tenses. I'm not correcting them, either.